

No, why would give sending SMS give access to your contact list? The carrier has no system access to the phone contacts app.
Edit: The phone contact app includes a lot more details than just the number. Names, alternative numbers, associated email addresses etc are all in the contacts app and potentially accessible to WhatsApp.
What the carrier has is no different to what WhatsApp gets when you use a number on their service.










An SMS app provided by the carrier? That seems highly unusual.